Numbers

Estimation

The process of approximating or rounding off numbers to avoid complicated calculations is known as Estimation.

We will learn the following types estimations:

• Rounding off/Estimation of numbers
• Estimating Sum
• Estimating Difference
• Estimating Product
• Estimating Quotient

Rounding off/Estimation of numbers:

Rounding off to the nearest tens:

• If the number has 1, 2, 3, or 4 at its unit place, round down the number.
• If the number has 5, 6, 7, 8, or 9 at its unit place, round up the number.
• To round off any number nearer to the tens, just consider its last two digits, that is. tens place and unit place digits.

Example:

Question: Round off 24836 to its nearest tens.

Answer: Here, the last two digits of 24836 are ⟶ 3 and 6.

At the unit place, the number is 6. So, we need to round up the number.

Replace the number 36 by 40.

The number 36 is nearest to 40 than 30.

So, 24836 rounded to nearest tens is 24840.

Following are some examples of rounding off to the nearest ten:

    4622 ⟶ 4620       26655 ⟶ 26660       637649 ⟶ 637650

Rounding off to the nearest hundreds:

• If the number has 0, 1, 2, 3 or 4 at its tens place, round down the number.
• If the number has 5, 6, 7, 8 or 9 at its tens place, round up the number.
• To round off any number nearest to the hundreds, just consider its last three digits, that is. hundred place, tens place and unit place digits.

Example:

Question: Round off 24836 to the nearest hundred.

Answer: Here, the last three digits of 24836 are ⟶ 836.

Tens place has number 3. So, we need to round down the number.

Replace the number 836 by 800.

Before 836 the nearest hundred number is 800.

So, 24836 rounded to the nearest hundred is 24800

Some more examples of rounding off to the nearest hundred are:

    4622 ⟶ 4600       26655 ⟶ 26700       637649 ⟶ 637600

Rounding off to the nearest thousand:

• If the number has 0, 1, 2, 3 or 4 at its hundreds place, round down the number.
• If the number has 5, 6, 7, 8 or 9 at its hundreds place, round up the number.
• To round off any number to its nearest thousands, just consider its last four digits, i.e., thousands place, hundreds place, tens place, and units place numbers.

Example:

Question: Round off 24836 to its nearest thousand.

Answer: Here, the last four digits are 24836 ⟶ 4836.

Hundreds place has number 8. So, we need to round up the number.

Replace the number 4836 by 5000.

After 4836 the nearest thousand number is 5000.

So, 24836 rounded to the nearest thousand is 25000.

Some more examples of rounding off to the nearest thousand are:

    4622 ⟶ 5000       26655 ⟶ 27000       637649 ⟶ 638000

So, we get:

• 24836 rounded to the nearest tens is 24840.
• 24836 rounded to the nearest hundred is 24800.
• 24836 rounded to the nearest thousand is 25000.

Estimating Sum or Difference

• To estimate sum or difference, first we need to round off addends/minuend and subtrahend.
• Rounded off each number to the appropriate place of smaller addends.
• Rounded off each number to the appropriate place according to the subtrahend.

Example:

Question 1: Estimate the sum 15,835 + 4,573.

Answer:

Step 1: Identify a smaller number.

    15,835 > 4,573 ⟶ (smaller number has 4-digits)

Step 2: Rounding off each number to the nearest hundred.

    15,835 Rounds off to ⟶ 15,800

    4,573 rounds off to   ⟶ 4,600

Step 3: Add.

So, estimated sum is 15,800 + 4,600 = 20,400

Check estimated answer:

Add the original numbers:

If we round off the original sum to the nearest hundreds, we get: 20,400.

If we rounded off addends to the nearest tens, we get a more appropriate estimation but the calculation will not be as quick.

Question 2: Estimate: 24,782 − 3,669.

Answer:

Step 1: Subtrahend has 4-digits

    24,782 > 3,669

Step 2: Rounding off each number to the nearest hundred.

    24,782 Rounds off to ⟶ 24,800

    3,669 rounds off to ⟶ 3,700

Step 3: Subtract.

So, estimated difference is 24,800 − 3,700 = 21,100

Check estimated answer:

Subtract original numbers:

If we round off the original difference to the nearest hundreds, we 21,100.

Estimating Product

To make multiplication easy, round off each number to its greatest place.

Example:

Question: Estimate: 3,781 × 295

Answer:

Step 1: Round off each factor to its greatest place.

    3,781 Round off to thousands ⟶ 4,000

    295 Round off to hundreds ⟶ 300

Step 2: Multiply

So, estimated product is 4,000 × 300 = 12,00,000

Check estimated answer:

Multiply the original numbers:

Estimating Quotient

To make division easy, round off the numbers to the same place.

Example:

Question: Estimate: 5,875 ÷ 697

Answer: Round off the number to the nearest thousand.

    5,875 Round off to ⟶ 6,000

    697 Round off to ⟶ 1,000

Now, divide.

=

Check estimated answer:

Divide the original numbers.

=

Use of estimation in real life

• To quickly guess the answer of the calculation between larger numbers.
• Estimation helps us to save time.
• Estimation helps us to save money.
• Estimation is used in various industries such as news, social media, weather department, share market, etc.